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Abstract

We study the dynamics of propagation of the pulse train modeled by truncated cnoidal-type wave in a nonlinear dispersion-managed (DM) fiber. Computer simulations permit to select fiber parameters and waveform to ensure self-repeating of wave after the dispersion map period. It is shown that the long-period maps lead to the complicated chaotic behavior of cnoidal type wave, namely the Kolmogorov-Arnold-Moser (KAM) chaos.

Figures (3)

Phase portraits of the dn-type wave on the Poincaré sphere for 3 harmonics taken into account. B=23/2Im(SΩS*0), C=23/2Re(SΩS*0), Ω=2.The dispersion management period is L0=1.2L. a - L=0.1. The center of the pattern B=C=0,A=1 corresponds to a constant intensity. It is unstable stationary point of the map. Two stable periodic points in upper and lower parts correspond to truncated cnoidal waves, the upper is marked with an arrow. b - L=0.75, c - L=0.95, d - L=1.25.

The same, as in Fig. 1, but for the cn-type wave with 4 harmonics taken into account. A=2(S1/2ΩS*1/2Ω-S3/2ΩS*3/2Ω), C=2Re(S3/2ΩS*1/2Ω), Ω=2. The dispersion management periods are L=0.1, 1.4, 1.8, and 2.8 for pictures a–d.

Influence of higher harmonics on the cnoidal wave. The intensity distributions over 200 periods in a wave which is close to the cn-wave and has initial parameters S1/2Ω=cos(0.29)/√2, S3/2Ω=sin(0.29)/√2 are shown. a - 4 harmonics, L=0.1, b - 10 harmonics, L=0.1 c - 4 harmonics, L=3, d - 8 harmonics, L=2.4, e - same as b, but initial conditions are not symmetric S-3/2Ω=(1+0.2i)S3/2Ω, S-1/2Ω=(1+0.2i)S1/2Ω